The gas injection and brine displacement process is a critical step in the construction of salt cavern gas storage facilities. This process involves injecting natural gas into the annular space of the gas injection and production tubing, displacing brine within the cavern to achieve the desired gas storage. To enhance the efficiency of this gas injection and brine displacement process, a three-dimensional finite element model of the salt cavern gas injection and brine displacement was established using SOLIDWORKS. Finite element analysis software was then employed to simulate the effects of different operational parameters on the brine displacement process. The model was used to analyze variations in the gas-liquid interface height and the movement of sediment. The results indicate that increasing the injection pressure and gas flow rate significantly accelerates the downward movement of the gas-liquid interface, thereby improving the brine displacement efficiency. Conversely, increasing the diameter of the displacement pipe hinders the rapid expulsion of brine, and a reduced distance between the pipe outlet and the sediment plane increases the risk of sediment entrainment and clogging. Based on these findings, an optimal method for selecting gas injection parameters was proposed, and the effectiveness of the optimized parameter set was validated through field tests. This study provides theoretical support and practical significance for the gas injection and brine displacement operations in salt cavern gas storage construction.